Keypoint-Based SAR Structure From Motion via Riemannian Optimization

Structure-from-motion (SfM) is the concept of estimating both sensor pose and three-dimensional (3D) scene structure from input images. The difficulty with synthetic aperture radar (SAR) SfM stems from the non-linearity of radar imaging, making it hard to decouple and calculate radar pose and structure. Existing methods typically address this issue by simplifying the imaging process or introducing auxiliary data. In this paper, we propose to jointly solve radar pose and structure by formulating an optimization problem, which only needs two-dimensional (2D) SAR observations as input. The objective function is written as the summation of all reprojection errors established by the precise range-Doppler (RD) imaging model, with radar poses embedded into the transformations between the sensor and scene coordinate systems. The rotational components in radar poses are represented as matrices and constrained on the special orthogonal group <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SO</i>(3). A special orthogonal Riemannian conjugate gradient algorithm (SO-RCG) is then proposed to solve the optimization problem. The proposed algorithm preserves the orthogonality of rotation matrices and updates all variables iteratively. Furthermore, we deduce that only five degrees of freedom (DoFs) in radar pose are involved in determining the imaging results of targets. We also discuss the ambiguity issue in multiview SAR observation leading to local minimums and introduce strategies against ambiguity. Experimental results on real-measured and simulated datasets show that the proposed algorithm is effective on both near- and far-field cases, and can be applied to both side-looking and squint SAR.